1 - you will need first to identify your motherboard model to:
- check if memory upgrade can be performed
- whether you have to add new memory or replace the existing one (looks like you have an empty slot)
2 - once done, be sure you took note of memory format (SDRAM, DDR, DDR2 DDR3 or even something else)
3 - make the right decision based on answer to point #1 above and order
- when adding additional memory module, depending on chipset, you may have some constraint that could be, e.g. to add same memory size. Thus right decision could be to remove your 1GB module and buy one 4GB or 2*2GB
4 - once received... shut-down your server, unplug power cord and open the box
5 - again based on answer to point #1 above:
- plug the additional memory module
- or remove the existing one and replace with the new one
6 - close the box, plug power cord back and switch on your server
7 - enjoy benefit of new memory size

As a matter of joke, I answered to this one but as stated by Escorpiom, this forum is perhaps not the right place for such question (neither the "how to replace my network card?"). For this I would suggest that you rather go to hardware specialised forum, preferably one for beginner